Timeline for Union bound over infinitely many events
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 23, 2021 at 5:51 | vote | accept | Zur Luria | ||
| May 23, 2021 at 5:51 | comment | added | Zur Luria | I am still surprised that there seems to be no "clean" continuous approach here that doesn't reduce the problem to the discrete case. | |
| May 23, 2021 at 5:49 | comment | added | Zur Luria | So I figured out a similar way to use discrete methods, which might be equivalent to Iosif's answer below: Take an $n \times m$ grid of circle centers, and consider all circles with centers in the grid and radius either $r+\frac{1}{m}$ or $r-\frac{1}{m}$. We can get concentration for these circles and then use the fact that all radius $r$ circles contain and are contained in the circles of the nearest grid point. | |
| May 20, 2021 at 12:53 | answer | added | Iosif Pinelis | timeline score: 3 | |
| May 20, 2021 at 11:17 | comment | added | Daniel Paleka | How strong do you want the concentration to be? You can tile the torus with very small squares such that the boundary of each disk intersects a few squares, and then union bound the event "empirical density of each square is close to its expected density". | |
| May 20, 2021 at 9:06 | history | asked | Zur Luria | CC BY-SA 4.0 |